The phrase "district seat" refers to the main or central location that serves as the headquarters or administrative center of a particular district. Full definition
The candidates running for the 24th congressional district seat offered three distinct choices for voters in the first televised debate featuring all three candidates last night. (wrvo.org)
There's more intrigue in the development of the race for the 11th district seat in 2008. (voices.washingtonpost.com)